A262280 Number of ways to select a nonempty subset s from an n-set and then partition s into blocks of equal size.

0, 1, 4, 11, 29, 72, 190, 527, 1552, 5031, 18087, 66904, 266381, 1164516, 5215644, 23868103, 117740143, 609872350, 3268548406, 18110463455, 102867877414, 620476915965, 4005216028161, 25747549921338, 166978155172420, 1168774024335203, 8556355097320141

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..616

Formula

E.g.f.: exp(x) * Sum_{k>=1} (exp(x^k/k!)-1).

a(n) = Sum_{k=1..n} C(n,k) * A038041(k).

a(n) = A262320(n) - 1.

Example

a(3) = 11: 1, 2, 3, 12, 1|2, 13, 1|3, 23, 2|3, 123, 1|2|3.

Maple

b:= proc(n) option remember;
      add(1/(d!*(n/d)!^d), d=numtheory[divisors](n))
    end:
a:= n-> n! * add(b(k)/(n-k)!, k=1..n):
seq(a(n), n=0..30);

Mathematica

b[n_] := b[n] = DivisorSum[n, 1/(#!*(n/#)!^#)&]; a[n_] := n!*Sum[b[k]/(n-k)!, {k, 1, n}]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Feb 15 2017, translated from Maple *)

Crossrefs

Cf. A038041, A262320.

Sequence in context: A220018 A131046 A109803 * A027968 A027970 A027972

Adjacent sequences: A262277 A262278 A262279 * A262281 A262282 A262283

Keyword

nonn

Author

Alois P. Heinz, Sep 17 2015

Status

approved